Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	modus ponens	1, 2	, , ,  ⊢
1	instantiation	3, 10, 13, 4	,  ⊢
	: , : , : , : , : , : , : , :
2	modus ponens	5, 6	,  ⊢
3	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
4	instantiation	17, 7, 8	,  ⊢
	: , :
5	instantiation	9, 10, 13	⊢
	: , : , : , : , : , :
6	generalization	11	,  ⊢
7	assumption		⊢
8	assumption		⊢
9	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
11	instantiation	12, 13, 14, 15	, ,  ⊢
	: , : , : , :
12	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
13	instantiation	16, 20, 21, 22	⊢
	: , : , :
14	instantiation	17, 27, 18	⊢
	: , :
15	instantiation	19, 20, 21, 22, 23, 24, 25	,  ⊢
	: , : , : , :
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
17	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
18	instantiation	26, 27, 28	⊢
	: , :
19	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
21	instantiation	31	⊢
	: , :
22	instantiation	29, 30	⊢
	:
23	instantiation	31	⊢
	: , :
24	assumption		⊢
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
27	instantiation	45, 33, 32	⊢
	: , : , :
28	instantiation	45, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32	instantiation	45, 36, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	45, 36, 37	⊢
	: , : , :
35	instantiation	45, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	45, 46, 40	⊢
	: , : , :
38	instantiation	41, 42, 43	⊢
	: , :
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
41	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
42	instantiation	45, 46, 44	⊢
	: , : , :
43	instantiation	45, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat4